# manufactured_solutions.jl
# Manufactured solutions for NSEMSolver validation and verification

"""
    SymbolicNSManufacturedSolution <: NSManufacturedSolution

Contains manufactured solution functions for validation.
"""
struct SymbolicNSManufacturedSolution <: NSManufacturedSolution
    dim::Int
    u_func::Function
    v_func::Function
    w_func::Function
    p_func::Function
    fx_func::Function
    fy_func::Function
    fz_func::Function
end

"""
    create_manufactured_solution(dim::Int=2) -> SymbolicNSManufacturedSolution

Create manufactured solution for Navier-Stokes equations.

# Arguments
- `dim::Int`: Problem dimension (2 or 3)

# Returns
- `SymbolicNSManufacturedSolution`: Complete manufactured solution
"""
function create_manufactured_solution(dim::Int=2)
    # Simplified manufactured solution without symbolic computation
    @warn "create_manufactured_solution is using simplified implementation without Symbolics"
    
    # Define simple analytical functions directly
    u_func = (x, y, z, t, nu) -> begin
        if dim == 2
            return cos(t) * sin(π * x) * cos(π * y)
        else
            # 3D divergence-free field: ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
            return cos(t) * sin(π * x) * cos(π * y) * cos(π * z)
        end
    end
    
    v_func = (x, y, z, t, nu) -> begin
        if dim == 2
            return -sin(t) * cos(π * x) * sin(π * y)
        else
            # 3D divergence-free field
            return sin(t) * cos(π * x) * sin(π * y) * cos(π * z)
        end
    end
    
    w_func = (x, y, z, t, nu) -> begin
        if dim == 3
            # For divergence-free: choose w to satisfy ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
            # ∂u/∂x = π * cos(t) * cos(π * x) * cos(π * y) * cos(π * z)
            # ∂v/∂y = π * sin(t) * cos(π * x) * cos(π * y) * cos(π * z)
            # So we need ∂w/∂z = -π * (cos(t) + sin(t)) * cos(π * x) * cos(π * y) * cos(π * z)
            # Therefore w = -(cos(t) + sin(t)) * cos(π * x) * cos(π * y) * sin(π * z)
            return -(cos(t) + sin(t)) * cos(π * x) * cos(π * y) * sin(π * z)
        else
            return 0.0
        end
    end
    
    p_func = (x, y, z, t, nu) -> 0.25 * (cos(2π * x) + cos(2π * y)) * cos(t)
    
    # Simplified forcing terms (normally derived from Navier-Stokes equations)
    fx_func = (x, y, z, t, nu) -> begin
        u_val = u_func(x, y, z, t, nu)
        return -sin(t) * sin(π * x) * cos(π * y) - nu * π^2 * u_val + 0.5 * sin(2π * x) * cos(t)
    end
    
    fy_func = (x, y, z, t, nu) -> begin
        v_val = v_func(x, y, z, t, nu)
        return -cos(t) * cos(π * x) * sin(π * y) - nu * π^2 * v_val + 0.5 * sin(2π * y) * cos(t)
    end
    
    fz_func = (x, y, z, t, nu) -> begin
        if dim == 3
            w_val = w_func(x, y, z, t, nu)
            return -sin(t) * sin(π * x) * sin(π * y) * cos(π * z) - nu * π^2 * w_val
        else
            return 0.0
        end
    end
    
    return SymbolicNSManufacturedSolution(dim, u_func, v_func, w_func, p_func, fx_func, fy_func, fz_func)
end

"""
    calculate_manufactured_u(sol::SymbolicNSManufacturedSolution, x, y, z, t) -> Float64

Calculate manufactured u-velocity at given coordinates and time.
"""
function calculate_manufactured_u(sol::SymbolicNSManufacturedSolution, x, y, z, t)
    return sol.u_func(x, y, z, t, 0.01)  # Using default viscosity
end

"""
    calculate_manufactured_v(sol::SymbolicNSManufacturedSolution, x, y, z, t) -> Float64

Calculate manufactured v-velocity at given coordinates and time.
"""
function calculate_manufactured_v(sol::SymbolicNSManufacturedSolution, x, y, z, t)
    return sol.v_func(x, y, z, t, 0.01)
end

"""
    calculate_manufactured_w(sol::SymbolicNSManufacturedSolution, x, y, z, t) -> Float64

Calculate manufactured w-velocity at given coordinates and time.
"""
function calculate_manufactured_w(sol::SymbolicNSManufacturedSolution, x, y, z, t)
    return sol.w_func(x, y, z, t, 0.01)
end

"""
    calculate_manufactured_p(sol::SymbolicNSManufacturedSolution, x, y, z, t) -> Float64

Calculate manufactured pressure at given coordinates and time.
"""
function calculate_manufactured_p(sol::SymbolicNSManufacturedSolution, x, y, z, t)
    return sol.p_func(x, y, z, t, 0.01)
end

"""
    calculate_manufactured_forcing(sol::SymbolicNSManufacturedSolution, x, y, z, t, nu) -> Tuple{Float64, Float64, Float64}

Calculate manufactured forcing terms at given coordinates, time, and viscosity.
"""
function calculate_manufactured_forcing(sol::SymbolicNSManufacturedSolution, x, y, z, t, nu)
    fx = sol.fx_func(x, y, z, t, nu)
    fy = sol.fy_func(x, y, z, t, nu)
    fz = sol.fz_func(x, y, z, t, nu)
    return (fx, fy, fz)
end

"""
    validate_manufactured_solution(sol::SymbolicNSManufacturedSolution; 
                                  test_point::Tuple=(0.5, 0.5, 0.5), 
                                  test_time::Float64=0.5) -> Bool

Validate that the manufactured solution satisfies the divergence-free condition.
"""
function validate_manufactured_solution(sol::SymbolicNSManufacturedSolution; 
                                       test_point::Tuple=(0.5, 0.5, 0.5), 
                                       test_time::Float64=0.5)
    
    x_val, y_val, z_val = test_point
    
    # Check divergence-free condition: ∇·u = 0
    # Since we're using simple analytical functions, we'll do a numerical check
    dx = 1e-6
    dy = 1e-6
    dz = 1e-6
    
    # Compute numerical derivatives
    u_plus_x = sol.u_func(x_val + dx, y_val, z_val, test_time, 0.01)
    u_minus_x = sol.u_func(x_val - dx, y_val, z_val, test_time, 0.01)
    dudx = (u_plus_x - u_minus_x) / (2 * dx)
    
    v_plus_y = sol.v_func(x_val, y_val + dy, z_val, test_time, 0.01)
    v_minus_y = sol.v_func(x_val, y_val - dy, z_val, test_time, 0.01)
    dvdy = (v_plus_y - v_minus_y) / (2 * dy)
    
    w_plus_z = sol.w_func(x_val, y_val, z_val + dz, test_time, 0.01)
    w_minus_z = sol.w_func(x_val, y_val, z_val - dz, test_time, 0.01)
    dwdz = (w_plus_z - w_minus_z) / (2 * dz)
    
    # Calculate divergence
    divergence = dudx + dvdy + dwdz
    
    # Check if approximately zero
    is_divergence_free = abs(divergence) < 1e-10
    
    if is_divergence_free
        println("✓ Manufactured solution satisfies ∇·u = 0 (|∇·u| = $(abs(divergence)))")
    else
        @warn "✗ Manufactured solution does not satisfy ∇·u = 0 (|∇·u| = $(abs(divergence)))"
    end
    
    return is_divergence_free
end

"""
    compute_manufactured_solution_error(sol::SymbolicNSManufacturedSolution,
                                       u_numerical::Array, v_numerical::Array, 
                                       w_numerical::Union{Array,Nothing}, p_numerical::Array,
                                       xx::Array, yy::Array, zz::Union{Array,Nothing}, 
                                       t_val::Float64) -> NamedTuple

Compute error norms between numerical and manufactured solutions.
"""
function compute_manufactured_solution_error(sol::SymbolicNSManufacturedSolution,
                                            u_numerical::Array, v_numerical::Array, 
                                            w_numerical::Union{Array,Nothing}, p_numerical::Array,
                                            xx::Array, yy::Array, zz::Union{Array,Nothing}, 
                                            t_val::Float64)
    
    # Evaluate exact solution
    u_exact = similar(u_numerical)
    v_exact = similar(v_numerical)
    p_exact = similar(p_numerical)
    
    if zz === nothing
        # 2D case
        for i in eachindex(xx), j in eachindex(yy)
            x, y = xx[i], yy[j]
            u_exact[i, j] = sol.u_func(x, y, 0.0, t_val, 0.01)
            v_exact[i, j] = sol.v_func(x, y, 0.0, t_val, 0.01)
            p_exact[i, j] = sol.p_func(x, y, 0.0, t_val, 0.01)
        end
        w_error_l2 = 0.0
        w_error_max = 0.0
    else
        # 3D case
        for i in eachindex(xx), j in eachindex(yy), k in eachindex(zz)
            x, y, z = xx[i], yy[j], zz[k]
            u_exact[i, j, k] = sol.u_func(x, y, z, t_val, 0.01)
            v_exact[i, j, k] = sol.v_func(x, y, z, t_val, 0.01)
            p_exact[i, j, k] = sol.p_func(x, y, z, t_val, 0.01)
        end
        
        if w_numerical !== nothing
            w_exact = similar(w_numerical)
            for i in eachindex(xx), j in eachindex(yy), k in eachindex(zz)
                x, y, z = xx[i], yy[j], zz[k]
                w_exact[i, j, k] = sol.w_func(x, y, z, t_val, 0.01)
            end
            w_error_l2 = sqrt(sum((w_numerical - w_exact).^2) / length(w_exact))
            w_error_max = maximum(abs.(w_numerical - w_exact))
        else
            w_error_l2 = 0.0
            w_error_max = 0.0
        end
    end
    
    # Compute error norms
    u_error_l2 = sqrt(sum((u_numerical - u_exact).^2) / length(u_exact))
    v_error_l2 = sqrt(sum((v_numerical - v_exact).^2) / length(v_exact))
    p_error_l2 = sqrt(sum((p_numerical - p_exact).^2) / length(p_exact))
    
    u_error_max = maximum(abs.(u_numerical - u_exact))
    v_error_max = maximum(abs.(v_numerical - v_exact))
    p_error_max = maximum(abs.(p_numerical - p_exact))
    
    return (
        u_l2_error = u_error_l2,
        v_l2_error = v_error_l2,
        w_l2_error = w_error_l2,
        p_l2_error = p_error_l2,
        u_max_error = u_error_max,
        v_max_error = v_error_max,
        w_max_error = w_error_max,
        p_max_error = p_error_max,
        total_l2_error = sqrt(u_error_l2^2 + v_error_l2^2 + w_error_l2^2 + p_error_l2^2)
    )
end

"""
    evaluate_manufactured_solution_on_grid(sol::SymbolicNSManufacturedSolution, 
                                          xx::Array, yy::Array, zz::Union{Array,Nothing}, 
                                          t_val::Float64) -> NTuple

Evaluate manufactured solution on entire grid.
"""
function evaluate_manufactured_solution_on_grid(sol::SymbolicNSManufacturedSolution, 
                                               xx::Array, yy::Array, zz::Union{Array,Nothing}, 
                                               t_val::Float64)
    if zz === nothing
        # 2D case
        u_exact = [sol.u_func(x, y, 0.0, t_val, 0.01) for x in xx, y in yy]
        v_exact = [sol.v_func(x, y, 0.0, t_val, 0.01) for x in xx, y in yy]
        w_exact = zeros(size(u_exact))
        p_exact = [sol.p_func(x, y, 0.0, t_val, 0.01) for x in xx, y in yy]
    else
        # 3D case
        u_exact = [sol.u_func(x, y, z, t_val, 0.01) for x in xx, y in yy, z in zz]
        v_exact = [sol.v_func(x, y, z, t_val, 0.01) for x in xx, y in yy, z in zz]
        w_exact = [sol.w_func(x, y, z, t_val, 0.01) for x in xx, y in yy, z in zz]
        p_exact = [sol.p_func(x, y, z, t_val, 0.01) for x in xx, y in yy, z in zz]
    end
    
    return u_exact, v_exact, w_exact, p_exact
end

"""
    evaluate_manufactured_forcing_on_grid(sol::SymbolicNSManufacturedSolution, 
                                         xx::Array, yy::Array, zz::Union{Array,Nothing}, 
                                         t_val::Float64, nu_val::Float64) -> NTuple

Evaluate manufactured forcing terms on entire grid.
"""
function evaluate_manufactured_forcing_on_grid(sol::SymbolicNSManufacturedSolution, 
                                              xx::Array, yy::Array, zz::Union{Array,Nothing}, 
                                              t_val::Float64, nu_val::Float64)
    if zz === nothing
        # 2D case
        fx_exact = [sol.fx_func(x, y, 0.0, t_val, nu_val) for x in xx, y in yy]
        fy_exact = [sol.fy_func(x, y, 0.0, t_val, nu_val) for x in xx, y in yy]
        fz_exact = zeros(size(fx_exact))
    else
        # 3D case
        fx_exact = [sol.fx_func(x, y, z, t_val, nu_val) for x in xx, y in yy, z in zz]
        fy_exact = [sol.fy_func(x, y, z, t_val, nu_val) for x in xx, y in yy, z in zz]
        fz_exact = [sol.fz_func(x, y, z, t_val, nu_val) for x in xx, y in yy, z in zz]
    end
    
    return fx_exact, fy_exact, fz_exact
end